The Minkowski dimension of boundary singular points in the Navier-Stokes equations. (English) Zbl 1419.35082
Singular point for a solution of the Navier-Stokes system is defined as a point where the velocity field is not continuous. The main result of the paper is that for solutions to the Navier-Stokes system in three dimensional domains, the Minkowski dimension (also called: entropy or box-counting dimension) of singular points at the boundary of the domain of is not greater than \(\frac{3}{2}\). Relations with regularity results and the dimension of interior singular points are discussed.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35Q30 | Navier-Stokes equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B50 | Maximum principles in context of PDEs |
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